so, i made a post a few days ago on r/askseddit about a situation that happened to me, but i think that i need a higher level advice because i'm confused.

At my local gym there this girl that imho is super cute. I'm a 20 y/o male. sadly never had a gf, still i tried some approaches and improved myself a lot in past 2 years.

I suck at daygame though. Following the advices i tried making eye contact and smiling too see if she was responsive.

First day she seemed not very interested but made a little of eye contact and, maybe it's just my imagination so i don't consider this to much of an IOI , she seemed to follow my training route(monday) on wednesday i saw her again and we made some eye contact and i smiled (too scared to approach though because of the place and the fact that a woman that i think is her mother was near her)

here's comes to friday when she was completely unresponsive. Sometimes looked back but i can't say if it's because she was looking for my eyes or because thought i was creepy.

may someone give me another advice on what to do? i know that a lot of people say "don't shit where you gym" and i can agree, but the only other time i saw her was friday evenin for a 0,1 seconds in the crowd , too random

plus: any advice on books or whatever to improve daygame is accepted. Thank you guys